Abstract

We present a model for the evolutionary dynamics of seed size when seedlings from large seeds are better competitors than seedling from small seeds and there is a trade-off between seed size and seed number. We first consider two limiting cases where seed size either has no effect on the competitive ability of seedlings, or where seedlings from larger seeds always win from seedlings from smaller seeds if together from the same germination site. In the first case there is a single evolutionary optimal seed size excluding all other, whereas in the second case there is an evolutionary stable seed polymorphism with a continuous variation of seed sizes where plants with small (but numerous seeds) survive by exploiting sites that by chance remain unoccupied by plants with larger (but less numerous) seeds. We investigate how these two cases connect to one another via intermediate levels of competitive asymmetry. We find that strong competitive asymmetry and high resource levels favor coexistence of plants with different seed sizes when seed and seedling survival is moderately low but large seeds have a substantial competitive advantage over small seeds. Assuming mutation-limited evolution and assuming that single mutations have only a small phenotypic effect, an initially monomorphic population with a single seed size will reach the final evolutionarily stable polymorphic state through a series of discrete evolutionary branching events. At each branching event, a given lineage already present in the population divides into two daughter lines, each with its own seed size. If precompetitive seed and seedling survival is high for small and large seeds alike, evolutionary branching may be followed by extinction of one or more lineages (including mass-extinction), and thus not necessarily gives rise to evolutionarily stable seed polymorphism. Various results presented here are model-independent and point the way to a more general evolutionarily bifurcation theory describing how the number and stability properties of evolutionary equilibria can change as a consequence of changes in model parameters.